Journal
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Volume 46, Issue 2, Pages 1633-1650Publisher
SIAM PUBLICATIONS
DOI: 10.1137/130942231
Keywords
Navier-Stokes-Korteweg system; vanishing capillarity limit; smooth solution; energy estimates
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Funding
- National Natural Science Foundation of China [11071057, 11271052, 11101331, 11331005, 11071093]
- Tian Yuan Special Foundation [11226029]
- FANEDD [201315]
- Science and Technology Program of Shaanxi Province [2013KJXX-23]
- Program for Changjiang Scholars and Innovative Research Team in University [IRT13066]
- Ministry of Education of China [20100144110001]
- Special Fund for Basic Scientific Research of Central Colleges [CCNU12C01001]
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In this paper, we consider the three-dimensional isentropic compressible fluid models of Korteweg type, called the compressible Navier-Stokes-Korteweg system. We mainly present the vanishing capillarity limit of the smooth solution to the initial value problem. Precisely, we first establish the uniform estimates of the global smooth solution with respect to the capillary coefficient.. Then by the Lions-Aubin lemma, we show that the unique smooth solution of the three-dimensional Navier-Stokes-Korteweg system converges globally in time to the smooth solution of the three-dimensional Navier-Stokes system as. tends to zero. Also, we give the convergence rate estimates for any given positive time.
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